static void mean_elements()
{
double fracT = fmod(T, 1);
/* Mean anomaly of sun = l' (J. Laskar) */
/*M = mods3600(129596581.038354 * T + 1287104.76154);*/
M = mods3600(129600000.0 * fracT - 3418.961646 * T + 1287104.76154);
M += ((((((((
1.62e-20 * T
- 1.0390e-17 ) * T
- 3.83508e-15 ) * T
+ 4.237343e-13 ) * T
+ 8.8555011e-11 ) * T
- 4.77258489e-8 ) * T
- 1.1297037031e-5 ) * T
+ 1.4732069041e-4 ) * T
- 0.552891801772 ) * T2;
#ifdef MOSH_MOON_200
/* Mean distance of moon from its ascending node = F */
NF = mods3600( 1739527263.0983 * T + 335779.55755 );
/* Mean anomaly of moon = l */
MP = mods3600( 1717915923.4728 * T + 485868.28096 );
/* Mean elongation of moon = D */
D = mods3600( 1602961601.4603 * T + 1072260.73512 );
/* Mean longitude of moon */
LP = mods3600( 1732564372.83264 * T + 785939.95571 );
/* Higher degree secular terms found by least squares fit */
NF += (((((z[5] *T+z[4] )*T + z[3] )*T + z[2] )*T + z[1] )*T + z[0] )*T2;
MP += (((((z[11]*T+z[10])*T + z[9] )*T + z[8] )*T + z[7] )*T + z[6] )*T2;
D += (((((z[17]*T+z[16])*T + z[15])*T + z[14])*T + z[13])*T + z[12])*T2;
LP += (((((z[23]*T+z[22])*T + z[21])*T + z[20])*T + z[19])*T + z[18])*T2;
#else
/* Mean distance of moon from its ascending node = F */
/*NF = mods3600((1739527263.0983 - 2.079419901760e-01) * T + 335779.55755);*/
NF = mods3600(1739232000.0 * fracT + 295263.0983 * T - 2.079419901760e-01 * T + 335779.55755);
/* Mean anomaly of moon = l */
/*MP = mods3600((1717915923.4728 - 2.035946368532e-01) * T + 485868.28096);*/
MP = mods3600(1717200000.0 * fracT + 715923.4728 * T - 2.035946368532e-01 * T + 485868.28096);
/* Mean elongation of moon = D */
/*D = mods3600((1602961601.4603 + 3.962893294503e-01) * T + 1072260.73512);*/
D = mods3600(1601856000.0 * fracT + 1105601.4603 * T + 3.962893294503e-01 * T + 1072260.73512);
/* Mean longitude of moon, referred to the mean ecliptic and equinox of date */
/*LP = mods3600((1732564372.83264 - 6.784914260953e-01) * T + 785939.95571);*/
LP = mods3600(1731456000.0 * fracT + 1108372.83264 * T - 6.784914260953e-01 * T + 785939.95571);
/* Higher degree secular terms found by least squares fit */
NF += ((z[2]*T + z[1])*T + z[0])*T2;
MP += ((z[5]*T + z[4])*T + z[3])*T2;
D += ((z[8]*T + z[7])*T + z[6])*T2;
LP += ((z[11]*T + z[10])*T + z[9])*T2;
#endif /* ! MOSH_MOON_200 */
/* sensitivity of mean elements
* delta argument = scale factor times delta amplitude (arcsec)
* cos l 9.0019 = mean eccentricity
* cos 2D 43.6
* cos F 11.2 (latitude term)
*/
}
int swi_moshplan2 (double J, int iplm, double *pobj)
{
int i, j, k, m, k1, ip, np, nt;
signed char FAR *p;
double FAR *pl, *pb, *pr;
double su, cu, sv, cv, T;
double t, sl, sb, sr;
struct plantbl *plan = planets[iplm];
T = (J - J2000) / TIMESCALE;
/* Calculate sin( i*MM ), etc. for needed multiple angles. */
for (i = 0; i < 9; i++)
{
if ((j = plan->max_harmonic[i]) > 0)
{
sr = (mods3600 (freqs[i] * T) + phases[i]) * STR;
sscc (i, sr, j);
}
}
/* Point to start of table of arguments. */
p = plan->arg_tbl;
/* Point to tabulated cosine and sine amplitudes. */
pl = plan->lon_tbl;
pb = plan->lat_tbl;
pr = plan->rad_tbl;
sl = 0.0;
sb = 0.0;
sr = 0.0;
for (;;)
{
/* argument of sine and cosine */
/* Number of periodic arguments. */
np = *p++;
if (np < 0)
break;
if (np == 0)
{ /* It is a polynomial term. */
nt = *p++;
/* Longitude polynomial. */
cu = *pl++;
for (ip = 0; ip < nt; ip++)
{
cu = cu * T + *pl++;
}
sl += mods3600 (cu);
/* Latitude polynomial. */
cu = *pb++;
for (ip = 0; ip < nt; ip++)
{
cu = cu * T + *pb++;
}
sb += cu;
/* Radius polynomial. */
cu = *pr++;
for (ip = 0; ip < nt; ip++)
{
cu = cu * T + *pr++;
}
sr += cu;
continue;
}
k1 = 0;
cv = 0.0;
sv = 0.0;
for (ip = 0; ip < np; ip++)
{
/* What harmonic. */
j = *p++;
/* Which planet. */
m = *p++ - 1;
if (j)
{
k = j;
if (j < 0)
k = -k;
k -= 1;
su = ss[m][k]; /* sin(k*angle) */
if (j < 0)
su = -su;
cu = cc[m][k];
if (k1 == 0)
{ /* set first angle */
sv = su;
cv = cu;
k1 = 1;
}
else
{ /* combine angles */
t = su * cv + cu * sv;
cv = cu * cv - su * sv;
sv = t;
}
}
}
/* Highest power of T. */
nt = *p++;
/* Longitude. */
cu = *pl++;
su = *pl++;
for (ip = 0; ip < nt; ip++)
{
cu = cu * T + *pl++;
su = su * T + *pl++;
}
sl += cu * cv + su * sv;
/* Latitiude. */
cu = *pb++;
su = *pb++;
for (ip = 0; ip < nt; ip++)
{
cu = cu * T + *pb++;
su = su * T + *pb++;
}
sb += cu * cv + su * sv;
/* Radius. */
cu = *pr++;
su = *pr++;
for (ip = 0; ip < nt; ip++)
{
cu = cu * T + *pr++;
su = su * T + *pr++;
}
sr += cu * cv + su * sv;
}
pobj[0] = STR * sl;
pobj[1] = STR * sb;
pobj[2] = STR * plan->distance * sr + plan->distance;
return OK;
}
static int
dargs (double J, struct plantbl *plan)
{
double T2, w;
if (J == Jlast)
return 0;
T = (J - JD2000) / 36525.0;
T2 = T * T;
/* Mean anomaly of sun = l' (J. Laskar) */
w = mods3600 (129596581.038354 * T + 1287104.76154);
w += ((((((((
1.62e-20 * T
- 1.0390e-17) * T
- 3.83508e-15) * T
+ 4.237343e-13) * T
+ 8.8555011e-11) * T
- 4.77258489e-8) * T
- 1.1297037031e-5) * T
+ 1.4732069041e-4) * T
- 0.552891801772) * T2;
sscc (10, STR * w, plan->max_harmonic[10]);
/* Mean distance of moon from its ascending node = F */
w = mods3600 ((1739527263.0983 - 2.079419901760e-01) * T + 335779.55755);
w = w + ((-9.646018347184e-06 * T2 /* F, t^4 */
- 1.138215912580e-03) * T /* F, t^3 */
- 1.312045233711e+01) * T; /* F, t^2 */
sscc (11, STR * w, plan->max_harmonic[11]);
/* Mean anomaly of moon = l */
w = mods3600 ((1717915923.4728 - 2.035946368532e-01) * T + 485868.28096);
w = w + ((-3.421689790404e-04 * T2 /* l, t^4 */
+ 4.768357585780e-02) * T /* l, t^3 */
+ 3.146734198839e+01) * T; /* l, t^2 */
sscc (9, STR * w, plan->max_harmonic[9]);
/* Mean elongation of moon = D */
w = mods3600 ((1602961601.4603 + 3.962893294503e-01) * T + 1072260.73512);
w = w + ((-2.905334122698e-04 * T2 /* D, t^4 */
- 5.834100476561e-03) * T /* D, t^3 */
- 6.847070905410e+00) * T; /* D, t^2 */
sscc (12, STR * w, plan->max_harmonic[12]);
/* Mean longitude of moon, re mean ecliptic and equinox of date */
w = mods3600 ((1732564372.83264 - 6.784914260953e-01) * T + 785939.95571);
w = w + ((-8.466472828815e-05 * T2 /* L, t^4 */
+ 5.722859298199e-03) * T /* L, t^3 */
- 5.663161722088e+00) * T; /* L, t^2 */
sscc (13, STR * w, plan->max_harmonic[13]);
/* Mean longitudes of planets (Laskar, Bretagnon) */
/* Venus. */
w = mods3600 (210664136.4335482 * T + 655127.283046);
w += ((((((((
-9.36e-023 * T
- 1.95e-20) * T
+ 6.097e-18) * T
+ 4.43201e-15) * T
+ 2.509418e-13) * T
- 3.0622898e-10) * T
- 2.26602516e-9) * T
- 1.4244812531e-5) * T
+ 0.005871373088) * T2;
sscc (1, STR * w, plan->max_harmonic[1]);
/* Earth. */
w = mods3600 (129597742.26669231 * T + 361679.214649);
w += ((((((((-1.16e-22 * T
+ 2.976e-19) * T
+ 2.8460e-17) * T
- 1.08402e-14) * T
- 1.226182e-12) * T
+ 1.7228268e-10) * T
+ 1.515912254e-7) * T
+ 8.863982531e-6) * T
- 2.0199859001e-2) * T2;
sscc (2, STR * w, plan->max_harmonic[2]);
/* Mars. */
w = mods3600 (68905077.59284 * T + 1279559.78866);
w += (-1.043e-5 * T + 9.38012e-3) * T2;
sscc (3, STR * w, plan->max_harmonic[3]);
/* Jupiter. */
w = mods3600 (10925660.428608 * T + 123665.342120);
w += (1.543273e-5 * T - 3.06037836351e-1) * T2;
sscc (4, STR * w, plan->max_harmonic[4]);
/* Saturn. */
w = mods3600 (4399609.65932 * T + 180278.89694);
w += ((4.475946e-8 * T - 6.874806E-5) * T + 7.56161437443E-1) * T2;
sscc (5, STR * w, plan->max_harmonic[5]);
return 0;
}
static void moon1()
{
double a;
/* Mean longitudes of planets (Laskar, Bretagnon) */
Ve = mods3600( 210664136.4335482 * T + 655127.283046 );
Ve += ((((((((
-9.36e-023 * T
- 1.95e-20 ) * T
+ 6.097e-18 ) * T
+ 4.43201e-15 ) * T
+ 2.509418e-13 ) * T
- 3.0622898e-10 ) * T
- 2.26602516e-9 ) * T
- 1.4244812531e-5 ) * T
+ 0.005871373088 ) * T2;
Ea = mods3600( 129597742.26669231 * T + 361679.214649 );
Ea += (((((((( -1.16e-22 * T
+ 2.976e-19 ) * T
+ 2.8460e-17 ) * T
- 1.08402e-14 ) * T
- 1.226182e-12 ) * T
+ 1.7228268e-10 ) * T
+ 1.515912254e-7 ) * T
+ 8.863982531e-6 ) * T
- 2.0199859001e-2 ) * T2;
Ma = mods3600( 68905077.59284 * T + 1279559.78866 );
Ma += (-1.043e-5*T + 9.38012e-3)*T2;
Ju = mods3600( 10925660.428608 * T + 123665.342120 );
Ju += (1.543273e-5*T - 3.06037836351e-1)*T2;
Sa = mods3600( 4399609.65932 * T + 180278.89694 );
Sa += (( 4.475946e-8*T - 6.874806E-5 ) * T + 7.56161437443E-1)*T2;
sscc( 0, STR*D, 6 );
sscc( 1, STR*M, 4 );
sscc( 2, STR*MP, 4 );
sscc( 3, STR*NF, 4 );
moonpol[0] = 0.0;
moonpol[1] = 0.0;
moonpol[2] = 0.0;
/* terms in T^2, scale 1.0 = 10^-5" */
chewm( LRT2, NLRT2, 4, 2, moonpol );
chewm( BT2, NBT2, 4, 4, moonpol );
f = 18 * Ve - 16 * Ea;
g = STR*(f - MP ); /* 18V - 16E - l */
cg = cos(g);
sg = sin(g);
l = 6.367278 * cg + 12.747036 * sg; /* t^0 */
l1 = 23123.70 * cg - 10570.02 * sg; /* t^1 */
l2 = z[24] * cg + z[25] * sg; /* t^2 */
l3 = z[26] * cg + z[27] * sg; /* t^3 */
l4 = z[28] * cg + z[29] * sg; /* t^4 */
moonpol[2] += 5.01 * cg + 2.72 * sg;
g = STR * (10.*Ve - 3.*Ea - MP);
cg = cos(g);
sg = sin(g);
l += -0.253102 * cg + 0.503359 * sg;
l1 += 1258.46 * cg + 707.29 * sg;
l2 += z[30] * cg + z[31] * sg;
l3 += z[32] * cg + z[33] * sg;
l4 += z[34] * cg + z[35] * sg;
g = STR*(8.*Ve - 13.*Ea);
cg = cos(g);
sg = sin(g);
l += -0.187231 * cg - 0.127481 * sg;
l1 += -319.87 * cg - 18.34 * sg;
l2 += z[36] * cg + z[37] * sg;
l3 += z[38] * cg + z[39] * sg;
l4 += z[40] * cg + z[41] * sg;
a = 4.0*Ea - 8.0*Ma + 3.0*Ju;
g = STR * a;
cg = cos(g);
sg = sin(g);
l += -0.866287 * cg + 0.248192 * sg;
l1 += 41.87 * cg + 1053.97 * sg;
l2 += z[42] * cg + z[43] * sg;
g = STR*(a - MP);
cg = cos(g);
sg = sin(g);
l += -0.165009 * cg + 0.044176 * sg;
l1 += 4.67 * cg + 201.55 * sg;
g = STR*f; /* 18V - 16E */
cg = cos(g);
sg = sin(g);
l += 0.330401 * cg + 0.661362 * sg;
l1 += 1202.67 * cg - 555.59 * sg;
l2 += z[44] * cg + z[45] * sg;
l3 += z[46] * cg + z[47] * sg;
g = STR*(f - 2.0*MP ); /* 18V - 16E - 2l */
cg = cos(g);
sg = sin(g);
l += 0.352185 * cg + 0.705041 * sg;
l1 += 1283.59 * cg - 586.43 * sg;
l2 += z[48] * cg + z[49] * sg;
l3 += z[50] * cg + z[51] * sg;
g = STR * (2.0*Ju - 5.0*Sa);
cg = cos(g);
sg = sin(g);
l += -0.034700 * cg + 0.160041 * sg;
l2 += z[52] * cg + z[53] * sg;
g = STR * (LP - NF);
cg = cos(g);
sg = sin(g);
l += 0.000116 * cg + 7.063040 * sg;
l1 += 298.8 * sg;
l2 += z[54] * cg + z[55] * sg;
/* T^3 terms */
sg = sin( STR * M );
l3 += z[56] * sg;
l4 += z[57] * sg;
g = STR * (2.0*D - M);
sg = sin(g);
cg = cos(g);
l3 += z[58] * sg;
l4 += z[59] * sg;
moonpol[2] += -0.2655 * cg * T;
g = g - STR * MP;
sg = sin(g);
l3 += z[60] * sg;
l4 += z[61] * sg;
g = STR * (M - MP);
l3 += z[62] * sin( g );
moonpol[2] += -0.1568 * cos( g ) * T;
g = STR * (M + MP);
l3 += z[63] * sin( g );
moonpol[2] += 0.1309 * cos( g ) * T;
g = STR * 2.0 * (D - M);
sg = sin(g);
l3 += z[64] * sg;
l4 += z[65] * sg;
g = STR * 2.0 * M;
sg = sin(g);
l3 += z[66] * sg;
l4 += z[67] * sg;
g = STR * (2.0*D - MP);
sg = sin(g);
l3 += z[68] * sg;
g = STR * (2.0*(D - M) - MP);
sg = sin(g);
l3 += z[69] * sg;
g = STR * (2.0*(D + M) - MP);
sg = sin(g);
cg = cos(g);
l3 += z[70] * sg;
moonpol[2] += 0.5568 * cg * T;
l2 += moonpol[0];
g = STR*(2.0*D - M - MP);
moonpol[2] += -0.1910 * cos( g ) * T;
moonpol[1] *= T;
moonpol[2] *= T;
/* terms in T */
moonpol[0] = 0.0;
chewm( BT, NBT, 4, 4, moonpol );
chewm( LRT, NLRT, 4, 1, moonpol );
g = STR*(f - MP - NF - 2355767.6); /* 18V - 16E - l - F */
moonpol[1] += -1127. * sin(g);
g = STR*(f - MP + NF - 235353.6); /* 18V - 16E - l + F */
moonpol[1] += -1123. * sin(g);
g = STR*(Ea + D + 51987.6);
moonpol[1] += 1303. * sin(g);
g = STR*LP;
moonpol[1] += 342. * sin(g);
g = STR*(2.*Ve - 3.*Ea);
cg = cos(g);
sg = sin(g);
l += -0.343550 * cg - 0.000276 * sg;
l1 += 105.90 * cg + 336.53 * sg;
g = STR*(f - 2.*D); /* 18V - 16E - 2D */
cg = cos(g);
sg = sin(g);
l += 0.074668 * cg + 0.149501 * sg;
l1 += 271.77 * cg - 124.20 * sg;
g = STR*(f - 2.*D - MP);
cg = cos(g);
sg = sin(g);
l += 0.073444 * cg + 0.147094 * sg;
l1 += 265.24 * cg - 121.16 * sg;
g = STR*(f + 2.*D - MP);
cg = cos(g);
sg = sin(g);
l += 0.072844 * cg + 0.145829 * sg;
l1 += 265.18 * cg - 121.29 * sg;
g = STR*(f + 2.*(D - MP));
cg = cos(g);
sg = sin(g);
l += 0.070201 * cg + 0.140542 * sg;
l1 += 255.36 * cg - 116.79 * sg;
g = STR*(Ea + D - NF);
cg = cos(g);
sg = sin(g);
l += 0.288209 * cg - 0.025901 * sg;
l1 += -63.51 * cg - 240.14 * sg;
g = STR*(2.*Ea - 3.*Ju + 2.*D - MP);
cg = cos(g);
sg = sin(g);
l += 0.077865 * cg + 0.438460 * sg;
l1 += 210.57 * cg + 124.84 * sg;
g = STR*(Ea - 2.*Ma);
cg = cos(g);
sg = sin(g);
l += -0.216579 * cg + 0.241702 * sg;
l1 += 197.67 * cg + 125.23 * sg;
g = STR*(a + MP);
cg = cos(g);
sg = sin(g);
l += -0.165009 * cg + 0.044176 * sg;
l1 += 4.67 * cg + 201.55 * sg;
g = STR*(a + 2.*D - MP);
cg = cos(g);
sg = sin(g);
l += -0.133533 * cg + 0.041116 * sg;
l1 += 6.95 * cg + 187.07 * sg;
g = STR*(a - 2.*D + MP);
cg = cos(g);
sg = sin(g);
l += -0.133430 * cg + 0.041079 * sg;
l1 += 6.28 * cg + 169.08 * sg;
g = STR*(3.*Ve - 4.*Ea);
cg = cos(g);
sg = sin(g);
l += -0.175074 * cg + 0.003035 * sg;
l1 += 49.17 * cg + 150.57 * sg;
g = STR*(2.*(Ea + D - MP) - 3.*Ju + 213534.);
l1 += 158.4 * sin(g);
l1 += moonpol[0];
a = 0.1 * T; /* set amplitude scale of 1.0 = 10^-4 arcsec */
moonpol[1] *= a;
moonpol[2] *= a;
}
/* Compute final ecliptic polar coordinates
*/
static void moon4()
{
moonpol[2] /= AUNIT / 1000;
moonpol[0] = STR * mods3600( moonpol[0] );
moonpol[1] = STR * moonpol[1];
}